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Home/Chain Registry/Block #2,174,558

Block #2,174,558

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/23/2017, 11:45:39 PM Β· Difficulty 10.9130 Β· 4,671,058 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
f25fd3c6b41ee7e370568cc704bda127bc08159a1841d0f69248be019d1b872a
View on Chainz β†—

Difficulty

10.913013

Transactions

1

Size

201 B

Version

2

Bits

0ae9bb3c

Nonce

691,543,029

Timestamp

6/23/2017, 11:45:39 PM

Confirmations

4,671,058

Merkle Root

b2c41463d8674364bfa027b5ebe690fea3aa30b54cef49ae6e612df8a7077680
Transactions (1)
Coinbaseb2c41463d86743…612df8a7077680
1 in β†’ 1 out8.3800 XPM110 B
AK6EwBb2…A49Bo4Eh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.808 Γ— 10⁹⁸(99-digit number)
18088381088807239987…94114428247235624960
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.808 Γ— 10⁹⁸(99-digit number)
18088381088807239987…94114428247235624959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.808 Γ— 10⁹⁸(99-digit number)
18088381088807239987…94114428247235624961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.617 Γ— 10⁹⁸(99-digit number)
36176762177614479975…88228856494471249919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.617 Γ— 10⁹⁸(99-digit number)
36176762177614479975…88228856494471249921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
7.235 Γ— 10⁹⁸(99-digit number)
72353524355228959950…76457712988942499839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.235 Γ— 10⁹⁸(99-digit number)
72353524355228959950…76457712988942499841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.447 Γ— 10⁹⁹(100-digit number)
14470704871045791990…52915425977884999679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.447 Γ— 10⁹⁹(100-digit number)
14470704871045791990…52915425977884999681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.894 Γ— 10⁹⁹(100-digit number)
28941409742091583980…05830851955769999359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.894 Γ— 10⁹⁹(100-digit number)
28941409742091583980…05830851955769999361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2174558

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock f25fd3c6b41ee7e370568cc704bda127bc08159a1841d0f69248be019d1b872a

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,174,558 on Chainz β†—
Circulating Supply:58,009,374 XPMΒ·at block #6,845,615 Β· updates every 60s
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